Problem #8: Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel.Suppose that X has the following probability density function (called the Rayleigh probability density function).x > 0f(x) = {(x10²) e-x²7/(20²)otherwise(a) If 0 = 108, find the probability that the vibratory stress is between 95 and 218.(b) If = 108, then 81% of the time the vibratory stress is greater than what value?

Answered: Let X denote the vibratory stress (psi)…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Problem 7: Let X be a continuous random variable with the probability density for f(x) = 3x2 values of x in [0,1], and f(x) = 0 elsewhere. Compute the expected value and variance of X.
Problem 1. A continuous random variable X is defined by f(x)=(3+x)^2/16 -3 ≤ x ≤ -1 =(6-2x^2)/16 -1 ≤ x ≤ 1 =(3-x^2)/16 -1 ≤ x ≤ 3 a)Verify that f(x) is density. b)Find the Mean
Question 10 The joint probability density function of X and Y is given by
QUESTION 11 The probability density function, f(x), for any continuous random variable X, represents: a. all possible values that X will assume within some interval a ≤ x ≤ b. b. the probability that X takes on a specific value x. c. the height of the density function at x. d. None of these choices.
Rework problem 16 in section 4.2 of your text, involving drawing markers from a box of markers with ink and markers without ink. Assume that the box contains 12 markers: 9 that contain ink and 3 that do not contain ink. A sample of 6 markers is selected and a random variable Y is defined as the number of markers selected which do not have ink. Find the probability density function. Be certain to list the values of Y in ascending order.
If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?
Question 1 : Suppose that the probability density function (p.d.f.) of the life (in weeks) of a certain part is f(x) = 3 x 2 (400)3 , 0 ≤ x < 400. (a) Compute the probability the a certain part will fail in less than 200 weeks. (b) Compute the mean lifetime of a part and the standard deviation of the lifetime of a part. (c) To decrease the probability in part (a), four independent parts are placed in parallel. So all must fail, if the system fails. Let Y = max{X1, X2, X3, X4} denote the lifetime of such a system, where Xi denotes the lifetime of the ith component. Show that fY (y) = 12 y 11 (400)12 , y > 0. Hint : First construct FY (y) = P(Y ≤ y), by noticing that {Y ≤ y} = {X1 ≤ y} ∩ {X2 ≤ y} ∩ {X3 ≤ y} ∩ {X4 ≤ y}. (d) Determine P(Y ≤ 200) and compare it to the answer in part (a)
Rework problem 16 in section 4.2 of your text, involving drawing markers from a box of markers with ink and markers without ink. Assume that the box contains 14 markers: 11 that contain ink and 3 that do not contain ink. A sample of 4 markers is selected and a random variable YY is defined as the number of markers selected which do not have ink. How many different values are possible for the random variable YY? Fill in the table below to complete the probability density function. Be certain to list the values of YY in ascending order.
Rework problem 16 in section 4.2 of your text, involving drawing markers from a box of markers with ink and markers without ink. Assume that the box contains 17markers: 15 that contain ink and 2 that do not contain ink. A sample of 3 markers is selected and a random variable Y is defined as the number of markers selected which do not have ink. How many different values are possible for the random variable Y? Fill in the table below to complete the probability density function. Be certain to list the values of Y in ascending order
QUESTION 10 Suppose f(x) = 1/4 over the range a ≤ x ≤ b, and suppose P(X > 4) = 1/2. What are the values for a and b? a. 2 and 6 b. Cannot answer with the information given. c. 0 and 4 d. Can be any range of x values whose length (b − a) equals 4. QUESTION 11 The probability density function, f(x), for any continuous random variable X, represents: a. all possible values that X will assume within some interval a ≤ x ≤ b. b. the probability that X takes on a specific value x. c. the height of the density function at x. d. None of these choices. QUESTION 12 Which of the following is true about f(x) when X has a uniform distribution over the interval [a, b]? a. The values of f(x) are different for various values of the random variable X. b. f(x) equals one for each possible value of X. c. f(x) equals one divided by the length of the interval from a to b.…
suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)
Question 1.2 Consider the function f (x) = (1/24(x^2 +1) 1 < or = x < or = 4) = (0 otherwise) Calculate P (x = 3) Calculate P (2 < or = x < or = 3) Question 1.3 Consider the function f (x) = (k - x/4 1 < or = x < or = 3) = (0 otherwise) which is being used as a probability density function for a continuous random variable x? a. Find the value of K b. Find P (x < or = 2.5)

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